The broad, long-term objectives of this research are the developments of statistical methods for the designs and analysis of clinical and epidemiological cancer studies, with or without genetic components. The specific aims of this competing renewal application include: (1) exploring semiparametric linear transformation models for univariate and multivariate continuous response variables, (2) developing graphical and numerical techniques to assess model adequacy and predictive accuracy under semi- parametric transformation models for right censored failure time data, (3) studying semiparametric transformation models for the analysis of univariate and multivariate failure time data subject to interval censoring, (4) pursuing statistically efficient and computationally feasible procedures for the analysis of accelerated failure time and accelerated hazards models with right censored data, (5) investigating variance-components models for the joint linkage and association analysis of complex disease traits in family studies, (6) handling complex data structures (e.g., family data, selective genotyping, and correlated genetic and environmental factors with missing values) in the analysis of haplotype-disease associations, and (7) addressing the issue of population stratification in genetic association studies of unrelated individuals. All these problems are motivated by the principal investigator's applied research experiences and are highly relevant to current cancer research. The proposed solutions are based on likelihood and other sound statistical principles. The large-sample properties of the new estimators and test statistics will be established rigorously via modern empirical process theory and semiparametric efficiency theory. Efficient and reliable numerical algorithms will be developed to implement the inference procedures. The proposed methods will be evaluated extensively through computer simulation and be applied to a large number of cancer studies, most of which are carried out at the University of North Carolina. User-friendly software will be freely available to the general public. This research will not only significantly advance the fields of survival analysis, longitudinal data analysis and statistical genetics, but will also provide valuable new tools to cancer researchers.